The Ridge Function Representation of Polynomials and an Application to Neural Networks  

作　　者：Ting Fan XIE Fei Long CAO 

机构地区：[1]Department of Information and Mathematics Sciences, China Jiliang University, Hangzhou 310018, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2011年第11期2169-2176,共8页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China （Grant No. 60873206） and Natural Science Foun- dation of Zhejiang Province of China （Grant No. Y7080235）

摘　　要：The first goal of this paper is to establish some properties of the ridge function representation for multivariate polynomials, and the second one is to apply these results to the problem of approximation by neural networks. We find that for continuous functions, the rate of approximation obtained by a neural network with one hidden layer is no slower than that of an algebraic polynomial.The first goal of this paper is to establish some properties of the ridge function representation for multivariate polynomials, and the second one is to apply these results to the problem of approximation by neural networks. We find that for continuous functions, the rate of approximation obtained by a neural network with one hidden layer is no slower than that of an algebraic polynomial.

关 键 词：Ridge function neural network POLYNOMIAL APPROXIMATION 

分 类 号：O174.14[理学—数学] TP18[理学—基础数学]